Designs and manufacturing methods for lightweight hyperdamping materials providing large attenuation of broadband-frequency structure-borne sound

ABSTRACT

A hyperdamping inclusion under constraint with large, broadband frequency damping properties is disclosed. The inclusion includes materials under near-buckling constraint such that fundamental eigenfrequency vanishes at near-buckling.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/587,189, filed Sep. 30, 2019, pending, which is a continuationapplication of U.S. patent application Ser. No. 15/447,934, filed Mar.2, 2017, now U.S. Pat. No. 10,458,501, issued Oct. 29, 2019, and claimspriority to U.S. Provisional Patent Application No. 62/302,405, filedMar. 2, 2016, which applications are hereby incorporated by reference intheir entirety for all purposes as if fully set forth herein.

BACKGROUND OF THE INVENTION Field of the Invention

Embodiments of the present invention relate to damping materials havingreduced weight than alternative material selections, and morespecifically hyperdamping materials and inclusions for application in avariety of structures.

Background

The absorption or attenuation of spectrally broadband vibration and waveenergy are goals that have called upon the efforts of researchersspanning diverse engineering and scientific disciplines over the years.While resonant phenomena can facilitate striking vibroacoustic energytrapping, many scenarios involve wide-band or stochastic energy sourcesfor which broadband energy capture is necessary. Typically, the onlyassured solution for broadband energy attenuation is to introduceexcessive mass between the dynamic energy source and the region/receiverof interest, which conflicts with requirements for many applications,such as vehicular systems, where added mass is detrimental toperformance and effectiveness. In addition, while input energies maycause vibrations at low frequencies associated with modal oscillations,practical structures transfer the energy to higher frequencies due tojoints, friction, and complex geometries, thus creating a ‘noiseproblem’ in a bandwidth most sensitive to humans through inevitablestructure-fluid interaction. Although conventional noise controltreatments such as lightweight, poroelastic media are well-suited todampen waves in this mid-to-high frequency range, they are ill-suited toattenuate low frequency vibrations and sound within typical sizeconstraints. As a result, there is a need for lightweight materials todampen spectrally broadband vibroacoustic energies.

To address the challenges, strategically architected material systemshave been explored that provide elastic and acoustic wave attenuationcapabilities not otherwise found in bulk structural materials. Amongthem, resonant metamaterials and phononic crystals exhibit opportunitiesto suppress vibration and wave energies due to tuned-mass-damper orbandgap effects. However, despite the advancements, the energyattenuation properties are reliant upon resonance- or bandgap-relatedphenomena that are often parameter sensitive and narrowband. Inaddition, many experimental realizations have been proposed using heavymaterials including metals and dense rubbers, which are inadequatesolutions in the numerous practical applications where treatment weightis a great penalty.

Building upon these ideas, periodic, elastic metamaterials leveraginginstability mechanisms are shown to yield remarkable wave propagationcontrol and energy absorption capabilities due to energy changesassociated with transitions among internal topologies. On the otherhand, these elastic systems are likewise realized by dense materialssuch as silicones or 3D-printed polymers that are ill-suited forapplications where increased treatment density comes at a high cost dueto the weight they add to finished products. Static stresses or exteriordisplacement constraints may also be needed to achieve the wavetailoring properties through the buckling instability, which preventsimplementing such metamaterials as absorbers of free field acousticenergy, in the operational mode similar to conventional poroelasticfoams. In fact, it is well-known that buckling instability-basedphenomena can enhance energy dissipation properties. Such anomalousdamping is due to a cancellation of the positive and negativestiffnesses, a design condition termed the elastic stability limit,which eliminates the fundamental natural frequency ω_(n)→0.

Yet, despite the recent advancements the reliance uponparameter-sensitive resonance-related phenomena, the use of densematerials, and possible need for exterior material constraints, makethese concepts insufficient solutions for applications demandinglightweight materials for broadband vibration and acoustic energycapture.

With a different material design perspective in mind, other recentstudies show that heterogeneous, poroelastic metamaterials can achieveconsiderable wave and/or vibration energy absorption. For instance,randomly embedding solid, metal inclusions into poroelastic foamsimproves the low frequency attenuation of the host media. Periodicallydistributing such inclusions also spawns bandgap phenomena tosubstantially increase low frequency vibroacoustic energy absorption via“trapped” mode effects. On the other hand, such advancements lackbroadband vibroacoustic energy dissipation in a lightweight systemdesign; instead, these poroelastic metamaterials excel at one or anotherof the individual performance measures.

BRIEF SUMMARY OF THE INVENTION

Accordingly, the present invention is directed to designs andmanufacturing methods for lightweight hyperdamping materials providinglarge attenuation of broadband-frequency structure-borne sound thatobviates one or more of the problems due to limitations anddisadvantages of the related art.

An advantage of the present invention is to provide a wave attenuationdevice, comprising an elastic metamaterial with at least two voids inthe elastic metamaterial where the elastic metamaterial under ageometric or stress constraint such that the elastic material is near abuckling condition

In another aspect of the present invention and further embodiment of thehyperdamping materials, a wave-attenuated structure, includes at leastone load-imparting wall; a wave attenuation device, comprising anelastic metamaterial having at least two voids in the elasticmetamaterial, the elastic metamaterial under a geometric or stressconstraint such that the elastic material is near a buckling condition;wherein the constraint is provided by the at least one load-impartingwall.

In another aspect of the present invention and further embodiment of thehyperdamping materials, a wave attenuation device includes a hollowmetal shell having a cross-sectional shape having a first dimension; andelastomeric material within the metal shell and having a cross-sectionalshape mimicking the first cross-sectional shape, the elastomericmaterial having a second dimension, the second dimension greater thanthe first dimension in a fully expanded state and a third dimension lessthan the first dimension in a compressed state within the metal shell.

Further embodiments, features, and advantages of the hyperdampingmaterials, as well as the structure and operation of the variousembodiments of the hyperdamping materials and devices, are described indetail below with reference to the accompanying drawings.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory only,and are not restrictive of the invention as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying figures, which are incorporated herein and form part ofthe specification, illustrate lightweight hyperdamping materialsaccording to principles of the present invention. Together with thedescription, the figures further serve to explain the principles of thelightweight hyperdamping materials described herein and thereby enable aperson skilled in the pertinent art to make and use the hyperdampingmaterials.

FIG. 1 a illustrates a side view of a hyperdamping inclusion accordingto principles of the present invention in disassembled form.

FIG. 1 b shows finite element model results that predict rotationalmotions for pre- and post-buckled designs.

FIG. 2A illustrates a side view of a hyperdamping inclusion according toprinciples of the present invention.

FIG. 2B illustrates spring forces associated with the illustratedhyperdamping inclusion.

FIG. 3 illustrates hyperdamping inclusions according to principles ofthe present invention embedded in a poroelastic material.

FIG. 4 is a finite element analysis plot for a hyperdamping inclusionaccording to principles of the present invention.

FIGS. 5A and 5B show a hyperdamping metamaterial specimen according toprinciples of the present invention prior to assembly.

FIG. 6 shows force transmissibility and absorption coefficientexperiment schematics.

FIG. 7 presents the results of force transmissibility amplitude andacoustic absorption coefficient

FIG. 8 shows that the broadband energy absorption and attenuation isprominent across the range of about 175-225 Hz.

FIG. 9 shows measurements of absorption coefficient.

FIG. 10 shows a comparison of eigenfrequency variation among the fourlowest eigenfrequencies and the corresponding mode shapes.

FIG. 11 illustrates eigenfrequency distribution and correspondingkinetic energy density of finite element analyses of materials accordingto principles of the present invention.

FIG. 12 shows force transducers used in experimental testing ofmaterials according to principles of the present invention.

FIG. 13 shows an impedance tube setup used in experimental testing ofmaterials according to principles of the present invention.

FIG. 14 is a graph illustrating absorption coefficient performance of anexemplary hyperdamping inclusion according to principles of the presentinvention versus a control inclusion and poroelastic foam alone.

FIG. 15 is a graph illustrating force transmissibility performance of anexemplary hyperdamping inclusion according to principles of the presentinvention versus a control inclusion and poroelastic foam alone.

FIG. 16 is a graph illustrating one-third octave ban measurements offorce transmissibility of an exemplary hyperdamping inclusion accordingto principles of the present invention versus poroelastic foam alone.

FIG. 17 illustrates an exemplary use for inclusions according toprinciples of the present invention.

FIG. 18 illustrates an exemplary use for inclusions according toprinciples of the present invention.

FIG. 19 illustrates an exemplary use for inclusions according toprinciples of the present invention

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to embodiments of the hyperdampingmaterials with reference to the accompanying figures, in which likereference numerals indicate like elements.

It will be apparent to those skilled in the art that variousmodifications and variations can be made in the present inventionwithout departing from the spirit or scope of the invention. Thus, it isintended that the present invention cover the modifications andvariations of this invention provided they come within the scope of theappended claims and their equivalents.

According to principles of the present invention, a new class ofengineered material system provides large, broadband-frequency energydamping properties—hyperdamping. Furthermore, the “engineering” of thematerial system according to principles of the present invention removesmass from the baseline, non-engineered material, such that these newhyperdamping materials are also lighter in weight than conventionalmaterials. These advantages—lightweight, and high damping across broadfrequency bandwidth—are desirable in numerous applications, includingvehicular, architectural, and infrastructural applications where suchperformance measures are typically at-odds. The important consequence ofthe elastic stability limit for hyperdamping systems according toprinciples of the present invention is that the damping ratio growswithout bound according to the classic relation for the fundamentalmodal damping ratio ζ=c/2mω_(n) where c and m are the modal dampingconstant and mass, respectively. Exemplary embodiments of design andfabrication procedures of hyperdamping materials according to principlesof the present invention are provided herein. In addition, experimentalmeasurements to demonstrate the performance of the various embodimentsare provided, although are not meant to be limited to the scope of theinvention.

An exemplary embodiment of “hyperdamping inclusion” 10 is illustrated inFIG. 1 . FIG. 1 (a) shows a hyperdamping inclusion 10 design accordingto principles of the present invention such that the elastomer element12 outer diameter D_(o) is greater than the inner diameter D_(i) of therigid, metal shell 11. FIG. 1(b) shows finite element model results thatpredict rotational motions for pre- and post-buckled designs. FIG. 2illustrates that a whole inclusion rotation is exhibited for increasingdegree of pre-compression upon inserting the elastomer/mass 12 into themetal shell 11, such that the inner elastic 14 or metallic center masses16 rotate. FIG. 3 illustrates a hyperdamping metamaterial 24 withembedded inclusions 20 in poroelastic media 24 to attenuate and absorbincident acoustic waves 26 and structural vibrations 28.

According to principles of the present invention, beam-likesub-components 18 are constrained in a way that causes them to nearlybuckle. For example, the elastomer inclusions 10 illustrated in FIGS. 1,2A and 2B include the radially arrayed beams 18 that are constrainedgeometrically by virtue of the outer shell 11 and inner lumped mass 14.For instance, the lumped mass 14 in FIG. 1 (a) is the central cylinderof elastomer out of which the radially-arrayed beams 18 extend. Suchnear-buckling can be realized in any material system that can be“architected” with beam-like internal geometries. This includes lasercutting into metal, wood, and so on such geometric features and havethose material components serve under constraint or static pre-load(that gives similar effect as constraint).

As illustrated, the exemplary device includes an elastomer inclusion.The elastomer inclusions are in a pattern with radially-arrayed beamsextending from a central, lumped elastomer mass. Namely, a soft,cylindrical and sculpted elastomer element is inserted into a metalshell 11 that has an inner diameter D_(i) smaller than the element'souter diameter D_(o), as illustrated in FIG. 1 a . This configuration isintended to load the elastomer topology at the elastic stability limit.FIG. 1 b shows finite element modeling results to illustrate stable,post-buckled topologies of the elastomer element if the constraintinduces a stress beyond criticality.

The elastomer/mass may be inserted into a shell that extends the samelength of the elastomer inclusion. This shell geometrically constrainsthe elastomer structure. For example, the outer elastomer diameter isgreater than the inner diameter of the shell. D_(o)/D_(i)>1. This chosendiameter ratio results in the radially-arrayed beams 18 of the inclusion10 nearly buckling under the geometric constraint. This strategicconstraint underlies the high damping, because beams 18 compressed atthis so-called “elastic stability limit” possess an infinitely largedamping ratio due to the elimination of the fundamental elasticstiffnesses. The uses of hyperdamping inclusions 10 according toprinciples of the present invention are many-fold. For example, asillustrated in FIG. 3 , the inclusions 20 may be embedded into a soft,poroelastic foam 24 where they attenuate structure-borne sound by thelocal, yet unusually greatly damped, resonances they undergo inconsequence to the effective stiffness and damping of the host foammaterial. Such applications would include acoustic barriers or panels inresidential or vehicular applications. According to principles of thepresent invention, it is also possible that the constraint condition isimposed by surrounding structure in lieu of the disclosed metal shell.That is, external stress can provide the near-buckling condition thatunderlies the damping properties of the beam-like structure of theelastomer element structure.

Depending on the design of internal elastomer elements, such as with orwithout a solid metal cylinder 16, buckling may or may not occur forgiven sizes of the metal shell 11, such as those illustrated in FIG. 2 .Such factors establish a versatile means for hyperdamping inclusion 10design and tuning.

Developed in this way and considering the shell 11 to be fixed, thehyperdamping inclusion is an extremely damped spring-mass, asillustrated schematically by FIG. 2B, having a vanishingly small naturalfrequency, where mass contributions are from the internal elastomer 14and other internal constituents, such as the metal cylinder shown inFIGS. 2A and 3 , in which the illustrated “springs” refer to thecritically-loaded, radially-arrayed beams 18 of the inclusion 10/20. Theinherent damping constant of this equivalent oscillator is thatassociated with the elastomer, and the relative impact of the finitedamping grows upon loading the inclusion at the elastic stability limit.To leverage the inclusion for wave energy capture, a hyperdampinginclusion 20 according to principles of the present invention may beembedded into poroelastic foam 24 where the total inclusion mass (i.e.the shell 11 and what is within) generates an additionalmass-spring-damper degree-of-freedom (DOF) due to the host media 24, asillustrated in FIG. 3 . Two resulting natural frequencies of thisequivalent two DOF system occur at a vanishingly-small value due to thecritically buckled constituent and at a (typically low) frequencyassociated with the total inclusion mass and host media properties.Thus, from an observer's perspective, the lightweight inclusionaccording to principles of the present invention responds dynamicallylike an extremely damped single DOF that yields massive vibroacousticenergy damping in a broad frequency bandwidth around and above the lownatural frequency associated with the total inclusion resonance. Thus,by leveraging a critically-loaded “hidden” DOF, the hyperdampingmetamaterial exhibits beneficial levels of vibration and wave energyattenuation and absorption using a lightweight design that interfaceswith the acoustic free field and does not rely on purely resonantphenomena to provide its effects. Here, the term “metamaterial” refersto an engineered material system that exhibits non-natural properties byvirtue of “hidden” internal constituents.

There is no limitation on the use of this concept with elastomericmaterials. The inclusions may be formed of any suitable elastomer,including, but not limited to, natural rubber, synthetic rubber, butylrubber, silicone rubber, butadiene rubber, neoprene, fluoroelastomer,thermoplastics, elastin, resilin, polysulfide, thermoset, polyurethane,or the like. The elastomeric material making up the inclusion accordingto principles of the present invention are not limited to this list. Thepattern may be formed by sculpting, injection molding, extrusion, 3-Dprinting, or the like. For example, the elastomer inclusion may be madeby providing the elastomer in a mold that is created in the negative ofthe desired inclusion shape. Thus, once the elastomer cures in the mold,the removed component possesses the design features of interest. A,central mass 14 or 16 may also be provided in the elastomer inclusion10, as shown in FIG. 2 . The central mass may include metal, ceramic,plastic, or other material providing suitable mass in the inclusion.

An exemplary process for fabricating hyperdamping materials according toprinciples of the present invention is described herein. The fabricationof the hyperdamping metamaterials is undertaken in several steps. Forexample, a 3D printer (such as, but not limited to, FlashForge CreatorPro) generates acrylonitrile butadiene styrene (ABS) molds that are thenegative of the desired elastomer elements. Silicone (such as, but notlimited to, Smooth-On, Inc., Mold Star 15S) is poured into the moldsthat may be previously sprayed with a release agent (such as, but notlimited to, Smooth-On, Inc., Ease Release 200). The samples are removedafter the recommended curing time for the material used has elapsed. Inthe exemplary embodiment, elastomer samples are cut to 19 mm length andallowed to set at room temperature for a sufficient time prior tofurther use. If the elastomer samples include interior metal cylinders(e.g., 6.35 mm outer diameter and 19 mm length) such as the samplesshown at right in FIG. 2 , the cylinders are held in place in the moldso that the silicone cures around the cylinder.

In prepared samples according to principles of the present invention,several samples of a given outer elastomer diameter D_(o) were produced(ranging from D_(o)∈[16.38,18.16] mm), whether with solid elasticinterior masses or with interior metal cylinders. The elastomer elementsproduced by this method exhibited a mean standard deviation of outerdiameter of 69 μm, which is on the order of the reported resolution ofthe 3D printer. The mean mass of the inclusions with elastomer andmetallic internal masses are 3.42 g and 8.04 g, respectively. Aluminumshells of inner diameter D_(i)=16.56 mm and thickness 1.25 mm are cut to19 mm lengths and the elastomer elements are carefully inserted into theshells. Sample inclusions 10 made according to this exemplary processinclude seven rotationally-symmetric voids 17, as shown in FIG. 1 .Inclusions made according to principles of the present invention caninclude any number of voids 17. Performance of inclusions with at leasttwo voids to realize an annular region around the interior mass suchthat the mass is capable of buckling under the displacement constraintimposed by the metal shell or other structure, are described herein.

A finite element (FE) model is useful to develop insight on inclusiontopological designs that maximize the effective damping properties ofthe components once embedded into the poroelastic media. An exemplary afinite element model may be composed using the commercial softwarepackage, such as COMSOL Multiphysics. The elastomer element designs ofinterest are those that are loaded around at the elastic stability limitonce constrained within the metal shells, such that the softeninginfluences are most prominent. In other words, the elastomer elementsare intended to be extremely close to the point of buckling to maximizethe effective damping properties when the inclusion (shell and elastomerelement) is embedded into the poroelastic foam. As previously shown, theresonance of the embedded inclusion in the foam is influenced by factorsthat consider such inclusions as equivalent lumped masses within adistributed elastic media. The rotational symmetry of the moldedelastomer designs considered here is based on the finding that appliedstress on an instability-driven periodic metamaterial induces a symmetrybreaking at the critical buckling stress, as illustrated by FIG. 1 b .Although several design parameters may be tailored to sculpt thetopology in ways that provide means to critically stress the elastomerelements, the focus in this example is on changing the diametric ratioD_(o)/D_(i) and the ratio of rotation angles α/β in an elastomer elementhaving seven voids, top of FIG. 4 . The rotational angle ratios α/βconsidered are set by the limits of fabrication using the current oravailable practice, while the diametric ratios D_(o)/D_(i) must be >1 toinduce buckling.

Referring to FIG. 4 , an illustration at the top right shows the designparameters of the diametric ratio D_(o)/D_(i) and the rotational angleratio α/β. The surfaces show the influence on the fundamentaleigenfrequency of the elastomer element by tailoring these parameters.The upper surface considers the elastomer element with the same internalelastomer mass, while the lower surface considers the metallic mass inthe elastomer element.

As observed in the finite element model results in FIG. 4 , the decreaseof the absolute value of the lowest eigenfrequency, which vanishes atthe buckling point, may span orders of magnitude via tailoring thediametric and rotational angle ratios. FIG. 4 presents results for casesin which the interior mass of the elastomer element is also elastomermaterial (upper surface 41) or the elastomer element contains themetallic interior mass (lower surface 43), which are the compositionsexhibited in FIG. 2 . It is observed that for a given selection ofrotational angle and diametric ratios, the inclusion with elastomerinner mass possesses the higher fundamental eigenfrequency. Bystrategically tailoring these ratios, the eigenfrequency can be adjustedfrom values in the 100s of Hz to the buckling point (0 Hz), whichstresses the elastomer element at the elastic stability limit. The shapeof this fundamental mode, as well as the first buckling mode, isexemplified in the finite element model results in FIG. 1 b . From themodel predictions presented in FIG. 4 , rotational angle ratios at thelimits of the current or available fabrication capabilities (α/β≈0.7)are required to buckle the elastomer elements within a reasonable amountof geometric constraint D_(o)/D_(i)<1.05. As observed empirically,values of such constraint above this amount may warp the elastomertopology at the contact surface with the metal shell 11, thus violatingthe finite element model assumptions and inhibiting uniform compressivestress at the contact. The results in FIG. 4 also indicate that thesamples with metallic inner masses buckle for smaller values of bothratios (lower surface 43) than those required for the samples having theelastomer masses (upper surface 41). Considering therotationally-symmetric unit of the inclusion highlighted by the dashedsection in the top right inset of FIG. 4 , each radially-arrayed beam isaxially constrained between the outer metal shell 11 and the inner mass.It is known that the presence of compliance in the boundary conditionsof axially-loaded beams increases the loads required to buckle the beam,which verifies the finding here that the comparatively rigid metallicinner masses require smaller diametric ratios to load the inclusions atthe elastic stability limit to exhibit desired hyperdamping effects.Using the insights derived from the finite element model analysis,hyperdamping metamaterials may be produced by embedding thestrategically designed inclusions 50 into 50.4 mm thick open cellpolyurethane foam 54 (such as that provided by Foam Factory, Inc., butnot limited thereto), the foam 54 being cylindrical and having adiameter of approximately 82 mm in two equal thicknesses. Referring toFIG. 5 , the foam 54 includes a centrally-located crevice 56, which maybe formed by extracted a portion of the foam 54 where a hyperdampinginclusion 50 according to principles of the present invention is to beplaced. The foam 54 and/or the hyperdamping inclusion 50 may be securedvia spray glue (such as, but not limited to, HDX Spray Adhesive). A foamcylinder 54 formed accordingly is illustrated in FIGS. 5A and 5B.Portions of the foam 54 extracted to form the crevice 56 or other foam,may be positioned in the crevice 56 after placement of the hyperdampinginclusion 50. The entire assembly may be secured, for example byapplying spray adhesive or glue into “one-piece”. In forming the“assembly”, glue or spray adhesive is lightly applied so as to notadversely impact the vibroacoustic properties of the polyurethane foam.By this fabrication, the resulting hyperdamping metamaterial specimenappears externally identical from the original cylinder of foam fromwhich it was derived, apart from a small seam of spray glue visiblearound the perimeter. In addition, by extracting the inner material, thefoam is not under additional stresses once re-assembled via the glue. Inthis example, the hyperdamping inclusions 50 constitute a 2% volume fillratio respecting the whole metamaterial volume, and result in aneffective metamaterial specimen density of 48 kg·m-3 (compared to thepolyurethane foam density 34 kg·m-3). This is significantly less thanthe effective density of recent metamaterials leveraging resonance- andbandgap-based phenomena (around 1500 kg·m-3 or >2000 kg·m-3) and is morecomparable to the density of various acoustical materials used inautomotive and aerospace applications.

FIG. 5 shows a hyperdamping metamaterial specimen according toprinciples of the present invention prior to assembly. FIG. 6 shows (b)force transmissibility and (c) absorption coefficient experimentschematics.

By a linear elastic finite model, the primary vibration modes of theinclusion 50 in the foam 54 occur around the frequency band 175 to 275Hz. For the metallic inner mass, these relevant resonances are at thelower end of this band, while for the elastomer mass they are at thehigher end. As a result, the greatest evidence of broadband energyabsorption provided by the hyperdamping metamaterials will be foundwithin this bandwidth. Above this frequency band, the modal densityincreases significantly per octave and the higher frequency modes aremostly associated with large deformations of the foam itself.Traditionally, periodic metamaterials are designed to leverage the lowerfrequency resonant modes for drastic vibroacoustic attenuation at thespecific eigenfrequencies. In contrast, the hyperdamping metamaterialaccording to principles of the present invention, using only a singleinclusion, facilitates strongly damped resonant properties in thisfrequency band, as well as at higher frequencies where the modal densitygrows. The result is a notably broadband, and hence robust, energytrapping and attenuation effect.

To characterize the impact of the hyperdamping inclusions, experimentswere conducted with the foam on its own, having been previously cut inhalf and re-assembled by spray glue, and also with a conventionalresonance-based metamaterial design that includes the foam and a singleinclusion consisting of lumped elastomer (not shown) without radiallyarrayed beams cured in the metal shell 11 referred to as the “resonantmetamaterial”. The conventional approach is also similar to the strategyemployed by the previous studies on poroelastic metamaterials wherelumped mass (often metal) inclusions have been considered. Allexperiments are carried out in an environmentally-controlled room at22.8° C. and 37% humidity. The force transmissibility through andacoustic absorption coefficient of the specimens are evaluated asschematically shown in FIG. 6 . The resulting force transmissibilitydata represent the averaged result from 80 independent measurements whenthe electrodynamic shaker (LabWorks, ET-140) was driven with white noisefiltered from 30 to 1500 Hz and data acquired using input and outputforce transducers (PCB Piezotronics, 208C01). The acoustic absorptiondata were derived from pressure measurements taken in the impedance tube65 with the acoustic source providing white noise from 50 to 1600 Hz.Results from the 80 independent measurements obtained from the twomicrophones 69 (PCB Piezotronics, 130E20) were averaged, in accordancewith ASTM E1050-12, to derive the absorption coefficient.

FIG. 7 presents the results of force transmissibility amplitude (leftcolumn) and acoustic absorption coefficient (right column) for theporoelastic foam itself (dotted curves), the resonant metamaterial(dashed curves, and see (c) top right illustration), and thehyperdamping metamaterial (solid curves, and see (c) top leftillustration) using a diametric ratio of D_(o)/D_(i)=1.051, elastomerinner mass, and rotational angle ratio α/β=0.70. According to the finiteelement model results shown in FIG. 4 , this diametric ratio is inexcess of the ideal design at the elastic stability limit, and thus thehyperdamping specimen used in the comparison of FIG. 7 is not optimized.Optimization of the hyperdamping specimen may, in one example, berealized by selecting diametric ratio and rotational angle ratio fromthe finite element model results that are exactly at the elasticstability limit, in which case the buckling point is predicted. Asdescribed above, the modes associated with large displacement of thetotal mass of the exemplary inclusion occur in the frequency band 175 to275 Hz, while modes below and above this range are mostly associatedwith large deformations of the foam itself. Thus, in FIG. 7(a), themeasurements of force transmissibility (FT) reveal great similarity inresponse trends at frequencies outside of this range, while in the rangethere are notable differences to consider. For instance, the narrowbandforce transmissibility shows that the resonant and non-optimizedhyperdamping metamaterials provide approximately similar reductionsacross the 175 to 275 Hz band, compared to the force transmissibility ofthe foam itself. This frequency band is associated with the principalresonant modes associated with large displacement of the total mass, asdescribed above. However, considering the ⅓-octave band results shown inFIG. 7(b), from 200 to 630 Hz, the hyperdamping metamaterial provides anaverage of 1.2 dB greater force transmissibility reduction than theresonant metamaterial.

In addition, the absorption coefficients in the narrowband and ⅓-octaveband comparisons of FIGS. 7(c) and 7(d), respectively, reveal similarenhancement of the acoustic wave attenuation by virtue of theinclusions. The results illustrated in FIGS. 7(c) and 7(d) show that anon-optimized hyperdamping metamaterial can provide comparable orgreater absorption of vibroacoustic energy than a counterpart, resonantmetamaterial, all the while the hyperdamping inclusion designconstitutes only 48% of the mass of the resonant inclusion.

FIG. 7 shows measurements of narrowband and ⅓-octave band results of(a,b) force transmissibility amplitude (FT) and (c,d) acousticabsorption coefficient. Comparison is made among the (dotted curves)poroelastic foam itself, (dashed curves) the resonant metamaterial withlumped elastomer and shell inclusion (see (c) top right illustration),and (solid curves)

Having assessed the merits of the hyperdamping concept with respect tothe conventional resonant metamaterial approach, we next evaluate theimpact of more effective hyperdamping inclusion design according toprinciples of the present invention as informed from the finite elementmodel results of FIG. 4 . In this way, we test the foundationalhypothesis of this research that inclusion designs nearest to theelastic stability limit cultivate the greatest damping effects. FIG. 8shows measurements of force transmissibility amplitude (FT). Dottedcurves denote results for the control specimen; solid curves denoteresults for the hyperdamping metamaterial with elastomer inner mass;dashed curves denote results for the hyperdamping metamaterial withmetallic inner mass. Narrowband and ⅓-octave band results for thehyperdamping specimen designs having diametric ratio (a,b)D_(o)/D_(i)=1.020, (c,d) D_(o)/D_(i)=1.035, and (e,f) D_(o)/D_(i)=1.066.

By the reductions in the force transmissibility amplitude with respectto the specimen consisting of only poroelastic foam, the measurements inthe top row in FIG. 8 show that the broadband energy absorption andattenuation is prominent across the range of about 175-225 Hz for thehyperdamping specimens having the metallic inner mass, FIG. 8(a), whilefor the specimens with elastic inner mass the energy capture is moreapparent around 200-275 Hz, FIG. 8 (c). The finite element model resultsin FIG. 4 indicate that the critical design point occurs for smallervalues of the diametric ratio D_(o)/D_(i) using the metallic innermasses, when the rotational angle ratio α/β is held constant. The forcetransmissibility measurements in both the narrowband and ⅓-octaveevaluations of FIG. 8 verify this design methodology. Namely, thehyperdamping metamaterial with metallic inner mass generates greaterbroadband energy dissipation for the smaller ratio D_(o)/D_(i)=1.020(29.1% mean reduction of FT in ⅓-octaves from 157 to 630 Hz with respectto the control specimen) while the specimen with elastomer inner massyields maximum broadband performance for a greater ratioD_(o)/D_(i)=1.035 (41.2% mean enhancement of FT reduction in ⅓-octavesfrom 250 to 630 Hz with respect to the control specimen). The reductionsto force transmissibility well above the primary resonances of theinclusions in the poroelastic material are due to the increasing modaldensity, which occurs above about 275 Hz, thus introducing means tomagnify the energy dissipation properties in the mid frequency range.These are significant increases in the broadband absorbed and attenuatedvibration energy, particularly considering that the hyperdampinginclusions account for only 2% of the total specimen volume.

These enhancements to the energy dissipation are reduced if thediametric ratio is changed to be deliberately away from the elasticstability limit. For example, the specimens having the metallic innermasses are less effective in the broadband reduction of FT whenD_(o)/D_(i)>1.020, FIGS. 8(c) and 8(e), which corresponds topost-buckled configurations of the elastomer element as observedempirically; specimens with elastomer inner masses have reduced energyattenuation performance for D_(o)/D_(i)>1.035, FIG. 5(e), which likewisecorresponds to post-buckling of the elastomer element. These resultsvalidate the hypothesis of this research that the hyperdamping effectsare due to the extreme softening of the inclusions and not simply tocompressing the inclusions beyond the buckling point.

FIG. 9 shows measurements of absorption coefficient. Dotted curvesdenote results for the poroelastic foam-only “control” specimen; solidcurves denote results for the hyperdamping metamaterial with elastomerinner mass; dashed curves denote results for the hyperdampingmetamaterial with metallic inner mass. Narrowband and ⅓-octave bandresults for the hyperdamping specimen designs having diametric ratio(a,b) D_(o)/D_(i)=1.035, (c,d) D_(o)/D_(i)=1.051, and (e,f)D_(o)/D_(i)=1.066.

The top row of FIG. 9 presents narrowband measurements of absorptioncoefficient, while the bottom row provides the corresponding ⅓-octaveband results. Of note, the polyurethane foam is itself very acousticallyabsorptive such that enhancement of this property using a single,embedded hyperdamping inclusion appears to be a challenging goal at theoutset. Yet, as seen in the top row of FIG. 6 , due to the presence ofthe hyperdamping inclusions the absorption coefficient of the baselineporoelastic foam is increased from frequencies of about 400 to 1400 Hz,across which the modal density is sufficiently great. This improvementis greater for the inclusions having metallic masses when employing thesmaller value of the diametric ratio, FIG. 6(a), D_(o)/D_(i)=1.035,which agrees with the FE model predictions. Using this inclusioncomposition, across the 500 to 1260 Hz ⅓-octave bands the mean absoluteenhancement of the absorption coefficient over control specimen levelsis 0.063, as shown in FIG. 9(b).

Hyperdamping inclusions with elastomer inner masses according toprinciples of the present invention are more effective at increasing theenergy dissipation (and hence absorption coefficient) for a greatervalue of diametric ratio, FIG. 9(c), yielding a mean absolute absorptioncoefficient improvement from the control specimen results of 0.045across the 500 to 1260 Hz ⅓-octave bands, FIG. 9 (d). Indeed, for bothof the exemplary designs that strategically leverage the hyperdampingeffect, the increase in the absorption coefficient over the controlspecimen is generally uniform across this broad frequency band. FIGS.9(e) and 9(f) show that the performances of the specimens are reducedfrom the peak achievements realized when the elastomer elements arecompressed around the elastic stability limit, for example, when theinclusions are constrained by diametric ratios greater than theexemplary values. The exceptional softening of the inclusion design isthe origin of the hyperdamping effects, which invests the metamaterialwith remarkable, broadband vibroacoustic energy dissipation propertiesusing a negligible change (2%) to the host media volume due to theembedded inclusion.

The finite element (FE) model to study the effective topologicalcomposition of the hyperdamping inclusions utilizes the geometryexemplified in FIG. 4 at the top inset, assuming plane strain conditionsapply for a first approximation of the principal eigenfrequencies andmodes. Material properties are therefore required for inner metalcylinders (if applicable) and for the elastomer elements. The steelmetal cylinders are modeled as a linear elastic material having density,Young's modulus, and Poisson's ratio, respectively, ρ=7800 kg·m-3,E=200×109 Pa, and v=0.30. Previous studies have indicated that similarvariants of the silicone used here to create the elastomer elements areadequately characterized using Neo-Hookean, hyperelastic materialmodels. In such cases, the strain energy density is expressed using

W=½μ₀(Ī ₁−3)+½K ₀(J−1)²

where μ₀ and K₀ are the initial shear and bulk moduli, J=det F is thedeterminant of the deformation gradient F=∂x/∂X found respecting thecurrent x and reference X configurations, and Ī₁=tr(F ^(T) F) iscomputed from the distortional tensor F=(J^(1/3)I)⁻¹F where I is theidentity matrix [1]. For the silicone material employed in thisresearch, representative parameters of μ₀=250 kPa and K₀=6.25 MPa areemployed in the FE computations while the density is ρ=1145 kg·m-3 asmeasured. The boundary conditions constrain the normal displacement ofthe elastomer element outer diameter in accordance with the constraintimposed by the ratio D_(o)/D_(i). An eigenfrequency analysis is carriedout to evaluate the influence upon the lower-order eigenfrequencies dueto the variation in the ratios α/β, which characterizes theunconstrained topology of the elastomer element, and D_(o)/D_(i) whichquantifies the nearness to the critical buckling stress upon theelastomer element topology. However, a design theme of the heretoforedescribed examples is that sculpted beams that support an internal massmust be arrayed radially from the inclusion center, otherwise thecompression provided by the geometric shell constraint would beprevented from causing a buckling of the topology. To illustrate thechange in the lower order eigenfrequencies in consequence to theconstraint imposed by the metal shell, FIG. 10 shows results from thisfinite element model for the case in which the rotational angle ratioα/β=0.70 while the diametric ratio D_(o)/D_(i) is varied. From thefinite element model results at right, it is evident that the second,third, and fourth eigenfrequencies do not significantly change due tothe critical stressing that occurs when the elastomer element topologyis designed to lead to buckling effects.

FIG. 10 shows a comparison of eigenfrequency variation among the fourlowest eigenfrequencies (at left) and the corresponding mode shapes (atright). The dotted curves at right indicate that the inner mass of theinclusion is metallic while the solid curves indicate results when theinner mass is composed of the elastomer material.

The finding that the second, third, and fourth eigenfrequencies do notsignificantly change due to the critical stressing may be explained bythe fact that these mode shapes are not rotationally symmetric, as shownin the right part of FIG. 10 , while the constraint that leads tobuckling is one which uniformly applies to the elastomer element aroundthe full perimeter.

A finite element model can be used to assess the distribution of thestructural eigenfrequencies and modes for the hyperdamping inclusiononce embedded into the polyurethane foam. By such an evaluation, one isable to more effectively assess the impact of the inclusions since thegreatest magnification of the damping effects are around the frequenciesassociated with these resonances, assuming they are significantlyexcited by the source input. As observed macroscopically, the resultwill be that these resonances, often associated with resonance-basedmetamaterials, will appear to be strongly damped.

The finite element model geometry is the same as the experimentalgeometry as detailed with respect to FIGS. 5 and 6 . In this model, thepolyurethane foam is considered to be a linear elastic material. Thus,poroelastic coupling is neglected, which is justified by the focus onsmall-amplitude, relatively low frequency force transmissibility andacoustic-elastic wave propagation, where the linear elasticcharacteristics of the polyurethane foam are more apparent. Thepolyurethane material properties are given to be ρ=30 kg·m-3, E=7×10⁴Pa, and v=0.41. The inclusion is modeled as an effective lumped mass ofuniform density, Poisson's ratio v=0.33, and high stiffness E=200×10⁹ Pain accordance with the assumption that it is only a cylindrical massembedded into the foam. The uniform density of this mass is thereforethe average mass of the inclusions for a given D_(o) (whether with innerelastomer or metallic cylindrical mass) divided by the inclusion volume.Consideration of the inclusion as a uniform body is theoreticallyjustified by the fact that the vanishing fundamental eigenfrequency ofthe hyperdamping inclusion means that the natural frequencies of thecomposite inclusion components (shell and elastomer element) as embeddedinto the foam media are primarily due to the total dynamic mass of thecomposite. This contrasts to considering the inclusion internals aspossessing additional degrees of freedom; under the unique condition ofthe buckling constraint which yields the hyperdamping effects, thevanishing principal stiffness contribution indicates that the effectiveresponse of the inclusion is significantly first-order and morerepresentative of a damping effect rather than like an additionalmass-spring-like degree of freedom.

In this finite element model, one circular surface of the metamaterialis fixed while the opposing circular face is free to move in thedirection normal to the surface but may not rotate. The results of thefinite element analyses are shown in FIG. 11 in terms of the kineticenergy density associated with each eigenfrequency. FIG. 11 illustrateseigenfrequency distribution and corresponding kinetic energy density ofthe mode. Squares indicate the results in which the lumped cylindricalinclusions are characterized according to the average density ofhyperdamping inclusions with elastomer inner masses, while the circlesdenote the result respecting hyperdamping inclusions with metallic innermasses. Thus, the plot provides information on the spectral distributionof the eigenmodes, as well as of the significance of the global systemenergy associated with the mode. The square data points indicate the FEmodel results in which the lumped cylindrical inclusions arecharacterized according to the average density of hyperdampinginclusions with elastomer inner masses (approximately 1238 kg·m-3),while the circles denote the results respecting hyperdamping inclusionswith metallic inner masses (approximately 2090 kg·m-3). The modes arefound to be the result of three primary phenomena. The lowest frequencymode in each case is associated with uniform (in-phase)compression/elongation of the metamaterial and inclusion. A midfrequency range of modes occurs wherein the inclusions are seen toexhibit large deformations and/or rotations within the foam, while thecorresponding eigenfrequencies occur at values corresponding to thetotal inclusion mass (and are thus distinct comparing the two inclusiontypes shown in FIG. 11 ). As a result of these large excursions of theinclusions, the greatest broadband damping effect is anticipated tooccur in this bandwidth around 175 to 325 Hz. Finally, a higherfrequency range of modes occurs characterized by large deformations ofthe foam while the inclusions are relatively stationary. Since there iscomparatively little displacement of the inclusions in contribution tothese modes, they occur at almost the same frequencies when consideringthe two types of inclusions evaluated in FIG. 11 . These resultsexemplify the fact that energy trapping occurs primarily at the lowerfrequencies associated with a select number of resonances possessinghigh kinetic energy density while at high frequencies the energy loss isdue to highly modal density resulting in stochastic-like vibrations thatresistively dissipate energy. Thus, this helps to explain why the energytrapping appearing in the force transmissibility experiments (FIGS. 4and 5 main text) is mostly localized in the frequency band <600 Hz whilethe absorption coefficient measurements (FIGS. 4 and 6 main text), whichdo not significantly excite lower frequency modes, give greaterindications of the high frequency losses associated with thelower-energy and higher frequency modes that are finely spaced apart inthe spectrum.

Force transmissibility experiments were conducted using the arrangementshown in FIG. 12 . The experiments are carried out on an opticalisolation table to prevent potential building motions from interferingwith the measurements. White noise filtered from 30 to 1500 Hz is usedto drive the electrodynamic shaker which acts on the input forcetransducer. An output force transducer is attached to a grounded, rigidaluminum frame. As illustrated in FIGS. 5 and 6 and as shown in FIG. 12, the force transducers are affixed to force expanders composed fromacrylic PMMA which are many orders of magnitude stiffer than thepolyurethane foam. The expanders' stiffness inhibits the possibilitythat the measured forces are different than those transmitted to thehyperdamping metamaterial specimens. The expanders also ensure that theforce is equally distributed across the full surfaces of the cylindricalmetamaterial specimen so as to evaluate only the one-dimensional forcetransmissibility property of the specimens through their thickness.Acquired data are sampled at 16384 Hz and are filtered from 20 to 2000Hz using a fourth-order bandpass infinite impulse response filter priorto further computation. Then, the force transmissibility of the 80independent measurements is determined and the average of the results istaken. One-third-octave band values are taken in conformance totraditional methods.

Absorption coefficient measurements were taken using the impedance tubesetup as shown in FIG. 13 . The tube length from acoustic source tospecimen surface is approximately 575 mm. The cylindrical metamaterialspecimens are mounted in a way such that the surface of the specimenwhich faces the propagating wave is normal to the direction of wavepropagation, ensuring that reflections are likewise normal. Data fromthe microphones are sampled at 51200 Hz and filtered from 20 to 2000 Hzusing a fourth-order bandpass infinite impulse response filter prior tofurther computation. Then, the acoustic absorption coefficient asdetermined from the 80 independent measurements is averaged.One-third-octave band values are computed according to traditionalmethods.

Although the elastomeric inclusions are described embedded inporoelastic foam, favorable damping properties exhibited through use ofthe elastomeric inclusions according to principles of the presentinvention do not require the surrounding poroelastic foam as illustratedin FIG. 3 . Instead the favorable damping properties are exhibited bythe constrained elastomer inclusion itself in whatever application it isemployed.

As another example application, this inclusion design may be directlyembedded into structural panels, such as dash or trim panels invehicular systems, where flexural vibrations and transmitted sound willbe extremely abated. Another example would be to use a constraintimposed by pre-load/stress (such as occupant weight on a seat cushion orengine weight on engine mount) to simplify the design to utilize onlythe inclusion component (i.e., no ‘shell’ component) while theradially-arrayed beams of the inclusion topology are nearly buckled inconsequence to the surrounding, pre-load/stress.

In fact, elastomeric materials are in common use as dampers, isolators,or fillers due to their large damping provided at mid-to-highfrequencies. An advantage of an elastomer inclusion according toprinciples of the present invention is that the sculpting of theelastomer removes material from the underlying non-engineered bulkelastomer material, making the hyperdamping materials lighter in weightthan their counterparts. Moreover, as shown in FIG. 3 , the hyperdampingmaterials attenuate greater structure-borne sound energy at lowfrequencies than the baseline non-engineered bulk elastomer materials.These factors show that elastomer inclusions according to principles ofthe present invention provides higher energy attenuation performanceusing less material mass than existing vibration/noise control treatmentapproaches.

In order to achieve the advantages of the present inclusion, the shellor “constraint” needs to be effectively rigid with respect to theinclusion material that is constrained to achieve the near-bucklingdescribed herein. To that end, the constraint does not need to be adifferent material. If the whole system is an elastomer and somewherewithin the elastomer is the architecture of the radially-arrayed beamsor similar beam constituents (they could be in a line of beams, forinstance similar to column arrangements in architectural contexts), thenwhen that whole elastomer system is under pre-load, the internal beamsub-components will be much more stressed than the whole and will nearlybuckle, as is desired to yield the hyperdamping effect. The choice ofthe constraint material can be chosen according to final engineeredproduct, provided that it achieves the desired pre-load.

As illustrated in FIGS. 14 and 15 , acoustic absorption coefficient andforce transmissibility are compared for cylindrical samples ofporoelastic foam with or without inclusions. One exemplary inclusion isconsidered a “control.” This exemplary control inclusion consists of asolid cylinder with elastomer that has been poured inside of a metalshell. The other exemplary inclusion considered is a “hyperdampinginclusion” made from the same “batch” of elastomer that was used for thecontrol inclusion, but made according to principles of the presentinvention. Yet, by the strategic sculpting and design, the hyperdampinginclusion is only about 48% of the mass of the control, indicating agreat weight savings.

Experimental measurements of acoustic absorption coefficient of thecontrol inclusion and the inclusion according to principles of thepresent invention are presented in FIG. 14 . Over almost all of thefrequencies, the hyperdamping inclusion provided increased absorptioncoefficient, and thus increased attenuation of air-borne acousticenergy, than both the poroelastic foam alone and the poroelastic foamwith the control inclusion. The noise reduction coefficient (NRC) from250 to 1,000 Hz of the control material is 0.50 in comparison to the NRCfrom 250 to 1,000 Hz for the hyperdamping material of 0.60. The narrowband measurements of force transmissibility through the samples areshown in FIG. 15 . FIG. 16 shows the corresponding one-third octave bandreductions in force transmissibility from the foam-only case.

The wide-band reductions in transmissibility seen in FIG. 15 as providedby the hyperdamping material/inclusion indicate a substantial increasein the structure-borne sound attenuation compared to the poroelasticfoam-only and the control material sample. The enhanced transmissibilityreductions are verified in the one-third octave band evaluations in FIG.16 , showing that the lighter weight hyperdamping material providessignificantly greater broadband vibration and acoustic energyattenuation. These exceptional properties—lightweight, and high dampingacross broad frequency bandwidth—are derived from the strategic designsand manufacturing methods of the hyperdamping inclusions as describedherein.

According to the design, the constituent that is stressed or loaded nearthe elastic stability limit is not limited to be an elastomer. Elastomeris utilized for proof-of-concept specimens due to its high compliancecompared to the metal shells that provide geometric constraint, whichresults in a ‘room-for-error’ in design. Stiff or metallic structures atthe elastic stability limit may be used to realize the hyperdampingeffect with appropriate control of tolerances. Materials softer than thepreviously-described elastomer for the hyperdamping inclusion, such as asculpted foam, may be used to realize the hyperdamping effect, givenappropriate attention to the fact that increased compliance of thesofter materials may result in the need for appropriate tolerancecontrol. Such flexibility for material selection enables broadimplementation opportunities.

Acoustic and/or elastic wave attenuation pertains to vibrations at allfrequencies, wave propagation at all frequencies, and transientphenomena such as impulsive and blast energies.

Acoustic and/or elastic wave attenuation by embedding or sculptinginclusions according to an aspect of the present invention within hostmedia (where the inclusions are the same material as the host media) andwhere the host media is under static pre-load, thus omitting use ofadditional constraint layer (e.g. metal shell described). Such“unconstrained” inclusion is illustrated in FIG. 1 separated from themetal shell. This implementation creates an internalone-degree-of-freedom internal system that can attenuate waves,vibrations, shock, and sound.

Such unconstrained device can be used in various applications, such as,but not limited to: architecting polystyrene foam acoustic/thermalinsulation with the beam sub-components that is pressed between studsand drywall in homes; concrete road surfaces with internal beam-likearchitectures that better attenuate road noise, and using similarconcepts in concrete road noise barriers that have high static pre-loadby virtue of their self-mass; sculpting the foam of a vehicle seat, suchas in cars, to have internal beam-like architecture so that when anoccupant rests on the seat, the pre-load provided by the individualserves to compress/constrain the beams near to their buckling pointresulting in a large suppression of energy to the seated occupant whenthe seat is excited by input vibrations and shock; sculpting carpets,pads, and other floor coverings that are underload by virtue of movingmass (people walking, objects rolling, etc), and building insulationmaterials for large sound transmission loss between rooms and residences

The inclusion geometry of beams that is created within thecarpet/pad/covering material can be designed to be constrained near tothe buckling point for a range of supported loads so that energy is lesstransferred through the carpet/pad/covering and to the floor below (suchas to an under-story residence); in other automotive, civil, aerospace,space, marine, or rail applications where all-metal realizations of theconcepts are desired, the geometry of slender internal beams may bemachined or otherwise cut into a host material such as a metal orplastic or wood, carpets and pads in vehicle systems, such as aircraftor automobiles, to deaden structure-borne noise (i.e. vibration and waveenergies that may also radiate to become sound).

Filler material for sandwich panels, such as filler for aluminumhoneycomb panels in aircraft, to dissipate operational vibrations. Whenthe system is subjected to excitations and loads, the internalcomponents undergo greater oscillation by virtue of the locally reducedstiffness (associated with the near buckling beam elements) and thusprovisioning the system with anomalous damping properties associatedwith these elements.

Acoustic and/or elastic wave attenuation by embedding or sculptinginclusions according to an aspect of the present invention and heldwithin constraining layers/shells, such as a metal shell, within hostmedia that are under static pre-load. The use of the constraining layeror shell is to provide for added resonant mass and generates atwo-degree-of-freedom internal system that can attenuate waves,vibrations, shock, and sound, with potential for greater effect at lowfrequencies than the above examples. These inclusions are thusself-enclosed and can be injected or otherwise inserted into othermedia.

Such constrained devices can be used in various applications, includingthose listed above, as well as, but not limited to: foam insulation inbuilding construction wherein such inclusions are a part of thefoam-making (blowing) process and become members of the foam layer; roomand office partitions, cubicle dividers, and so on with internalinclusions for enhancing noise insulation properties. An inclusionaccording to these principles provides for broadband and low frequencynoise control enhancement and thus may be used in any structure wheresuch frequency damping is desired.

Acoustic and/or elastic wave attenuation by embedding inclusions withinstructural members, where the latter members serve as components of agreater system. For example, inclusions according to principles of thepresent invention may be used within vehicle frame component, such asthe subframe, A- or B-pillars, and other automotive components; inaerospace/space components as in within sandwich panels (that are astaple aircraft construction) or within the stingers of aircraft wings,and in rail-transport frame members having hollow geometries. Theseinclusions may be inserted into all such geometries and be naturallycompressed within the host geometry. For instance, the subframes ofautomobiles often have cylindrical-like extruded geometries wherein aconventional cylindrical hyperdamping inclusion may be designed andembedded. Thus, when the host system is under acoustic/elastic waveexcitations, the embedded hyperdamping inclusions will effectivelyattenuate the energies prior to their delivery further downstream todelicate vehicle locations (such as an occupant seat attached to avehicle chassis).

Inclusions according to principles of the present invention may be usedin civil or structural engineering applications where C, U, and box-beammembers compose the structure. Into such C, U, or box channels can beinserted the inclusions that would be targeted to be under the desiredcompression constraint to yield near-buckling of the beam components.Thus, when the structure is under wind or seismic or machine-inducedloads (like HVAC on roof), the inclusions can abate transfer of theenergy into motions of the structure by the damping of energy at theinclusion.

Inclusions according to principles of the present invention may be usedin applications of seals, where the seal is compressed in order toprevent leakage of flow of liquid or gas but the compressed structuralpiece (such as a cap, door, or trim) is also desired to not vibrate dueto exterior structural or acoustic loads. Thus, the hyperdamping-typeseal may have a cross-section geometry that includes beam componentsthat when under the working condition of the seal (where it iscompressed) both provides the demanded flow prevention and enhancesdamping of the structural piece that compresses it down via the greaterdamping properties borne out by the compressed internal geometry.

Inclusions according to principles of the present invention may be usedas shock/vibration absorbers for electronics where the hyperdampinginclusions serve to support the load of the electronics while promotinglarge attenuation of the input energy from transmitting to the supportedlayer of electronics. The inclusions would be designed such that theirsupported load or pre-compression extent capitalizes on the hyperdampingphenomenon.

Examples of uses for inclusions according to principles of the presentinvention are illustrated in FIGS. 17-19 , and include vehicle panels,seats and in space launch vehicles. These examples are by no meansintended to be limiting.

For example, FIG. 17 illustrates elongated tubular inclusions 170according to principles of the present invention incorporated intovehicular structural panels. As can be appreciated from the figures, thetubular inclusions 170 include voids. The near buckling constraint onthe tubular inclusions may be provided by an external cylindrical shellor the near buckling constraint may be imparted by load provided bycomponents, such as walls 174, of the structural panel itself.

As illustrated in at least FIG. 18 , hyperdamping material includingappropriate voids to impart the beam-like properties according toprinciples of the present invention may be included in a structuraldesign, where the near buckling condition is provided by externalload-providing structures, such as spacing panels or walls at theboundary of the hyperdamping material 184.

As illustrated in at least FIG. 19 , hyperdamping inclusions includingappropriate voids to impart the beam-like properties according toprinciples of the present invention may be included in a structuraldesign for other vibration environments, such as space launch vehicles.As can be appreciated from the figures, the inclusions 190 includevoids. The near buckling constraint on the tubular inclusions may beprovided by an external shell or the near buckling constraint may beimparted by load provided by components, such as walls, of thestructural panel itself.

As employed here, “hyperdamping” indicates an unusually large proportionof damping forces, with respect to inertial and stiffness-based forces,in consequence to design- or constraint-based factors imposed upon anintelligently architected inclusion topology. In the presentimplementation, the selection of diametric ratio for a given elastomerelement topology enables the extreme softening which is characteristicof loading conditions at the elastic stability limit. Other researchershave realized similar anomalous dissipative phenomena via appliedcompressive stress, ferroelectric domain switching, and temperaturecontrol. Contrasting these approaches, the strategy employed here torealize hyperdamping within the poroelastic media is passive,non-destructive to the host material, and not subject to major deviationover time by hysteretic influences, thus making the proposedhyperdamping metamaterials more viable for practical applications.Moreover, this study focuses on the impact of an individual inclusionupon the resulting vibroacoustic properties of the metamaterial. Thiscontrasts with previous studies that have exemplified the roles ofperiodicity towards magnifying the energy absorption possible inresonant metamaterials or phononic crystals. Yet, based on theexperimental evidence described herein, substantial broadband energytrapping and attenuation is achievable even when employing just onehyperdamping inclusion at a 2% volume fill in the poroelastic media.

Principles of the present invention provide hyperdamping metamaterialsto realize broadband energy trapping and attenuation, while retainingthe advantages of a lightweight solution viable for diverse noise andvibration control applications. Because the hyperdamping effects are notreliant upon the resonance- or bandgap-based phenomena of conventionalmetamaterials and phononic crystals, the effectiveness of the energyattenuation is more robust for working conditions where the peakfrequencies of vibroacoustic energy may vary in time. In this way, thelightweight, hyperdamping metamaterials have practical benefits overcontemporary counterparts.

Embodiments of the present invention provide lightweight, hyperdampingmetamaterials that interface with the acoustic free field to achievelarge vibration and acoustic wave energy attenuation.

While various embodiments of the present invention have been describedabove, it should be understood that they have been presented by way ofexample only, and not limitation. It will be apparent to persons skilledin the relevant art that various changes in form and detail can be madetherein without departing from the spirit and scope of the presentinvention. Thus, the breadth and scope of the present invention shouldnot be limited by any of the above-described exemplary embodiments, butshould be defined only in accordance with the following claims and theirequivalents.

What is claimed is:
 1. A wave attenuation device, comprising: an elasticmetamaterial; at least two voids in the elastic metamaterial; theelastic metamaterial under a stress constraint such that the elasticmaterial is near a buckling condition.